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A062157 a(n) = 0^n-(-1)^n. 11
0, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Also the numerators of the series expansion of log(1+x). Denominators are A028310. - Robert G. Wilson v, Aug 14 2015

LINKS

Table of n, a(n) for n=0..101.

Wikipedia, Dirichlet eta function

Index entries for linear recurrences with constant coefficients, signature (-1).

FORMULA

a(n) = A000007(n) - A033999(n) = A062160(0, n). G.f.: x/(1+x).

a(n) = -[(n+2) mod (n+1)]*(-1)^n, with n>=0. - Paolo P. Lava, Aug 28 2007

Euler transform of length 2 sequence [ -1, 1]. - Michael Somos, Jul 05 2009

Moebius transform is length 2 sequence [ 1, -2]. - Michael Somos, Jul 05 2009

a(n) is multiplicative with a(2^e) = -1 if e>0, a(p^e) = 1 if p>2. - Michael Somos, Jul 05 2009

Dirichlet g.f.: zeta(s) * (1 - 2^(1-s)). - Michael Somos, Jul 05 2009

Also, Dirichlet g.f.: eta(s). - Ralf Stephan, Mar 25 2015

MATHEMATICA

PadRight[{0}, 120, {-1, 1}] (* Harvey P. Dale, Aug 20 2012 *)

Join[{0}, LinearRecurrence[{-1}, {1}, 101]] (* Ray Chandler, Aug 12 2015 *)

f[n_] := 0^n - (-1)^n; f[0] = 0; Array[f, 105, 0] (* or *)

CoefficientList[ Series[ x/(1 + x), {x, 0, 80}], x] (* or *)

Numerator@ CoefficientList[ Series[ Log[1 + x], {x, 0, 80}], x] (* Robert G. Wilson v, Aug 14 2015 *)

PROG

(PARI) {a(n) = if( n<1, 0, -(-1)^n )} /* Michael Somos, Jul 05 2009 */

(MAGMA) [0^n-(-1)^n: n in [0..100]] /* or */ [0] cat &cat[ [1, -1]: n in [1..80] ];; // Vincenzo Librandi, Aug 15 2015

CROSSREFS

Convolution inverse of A019590.

Sequence in context: A165596 A070238 * A103131 A112347 A057427 A178334

Adjacent sequences:  A062154 A062155 A062156 * A062158 A062159 A062160

KEYWORD

easy,sign,mult

AUTHOR

Henry Bottomley, Jun 08 2001

STATUS

approved

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Last modified July 21 16:46 EDT 2017. Contains 289643 sequences.